The supposed irrelevance of historical costs for rational decision making has been the subject of much interest in the economic literature. In this paper we explore whether individual decision making under risk is affected by the cost of the supplied information. Outside of the lab, it is difficult to disentangle the effect of the cost of information itself from the effect of self-selection by individuals who tend to gain the most from this information. We thus create an environment in the lab where subjects are offered additional, useful and identical information on the state of the world across treatments. By varying the cost of information we can distinguish between selection and sunk cost effects. We find a systematic effect of sunk costs on the manner in which subjects update their beliefs on the state of the world. Subjects over-weigh costly information relatively to free information, which results in a 'push' of beliefs towards the extremes. This shift does not necessarily lead to behavior more attuned with Bayesian updating.